genridge (version 0.7.0)

pca: Transform Ridge Estimates to PCA Space

Description

The function pca.ridge transforms a ridge object from parameter space, where the estimated coefficients are \(\beta_k\) with covariance matrices \(\Sigma_k\), to the principal component space defined by the right singular vectors, \(V\), of the singular value decomposition of the scaled predictor matrix, \(X\).

In this space, the transformed coefficients are \(V \beta_k\), with covariance matrices $$V \Sigma_k V^T$$.

This transformation provides alternative views of ridge estimates in low-rank approximations. In particular, it allows one to see where the effects of collinearity typically reside --- in the smallest PCA dimensions.

Usage

pca(x, ...)

Value

An object of class c("ridge", "pcaridge"), with the same components as the original ridge object.

Arguments

x

A ridge object, as fit by ridge

...

Other arguments passed down. Not presently used in this implementation.

Author

Michael Friendly

References

Friendly, M. (2013). The Generalized Ridge Trace Plot: Visualizing Bias and Precision. Journal of Computational and Graphical Statistics, 22(1), 50-68, doi:10.1080/10618600.2012.681237, https://www.datavis.ca/papers/genridge-jcgs.pdf

See Also

ridge

Examples

longley.y <- longley[, "Employed"]
longley.X <- data.matrix(longley[, c(2:6,1)])

lambda <- c(0, 0.005, 0.01, 0.02, 0.04, 0.08)
lridge <- ridge(longley.y, longley.X, lambda=lambda)

plridge <- pca(lridge)
traceplot(plridge)
pairs(plridge)
# view in space of smallest singular values
plot(plridge, variables=5:6)